Washington (CNN)Donald Trump dominates the Republican presidential field nationally and in New Hampshire, while he's locked in a tight race in Iowa with Texas Sen. Ted Cruz heading into Tuesday's Republican presidential debate, according to new CNN Poll of Polls averages.

A flurry of polls released in the last few days have pointed in sometimes conflicting directions as the first debate since the terror attacks in Paris and the shooting in San Bernardino approaches, but the Poll of Polls points to clear story lines emerging nationally and in the two states set to cast the first ballots of the 2016 presidential campaign.

The CNN Poll of Polls finds that across the five latest national, live-interviewer telephone polls, Trump tops Cruz 33% to 17% in the race for the Republican nomination. Behind Cruz, Florida Sen. Marco Rubio (12%) and retired neurosurgeon Ben Carson (11%) are the only other candidates with average support above 10%. Former Florida governor and one-time front-runner Jeb Bush averages 4%, New Jersey Gov. Chris Christie holds 3%, with businesswoman Carly Fiorina, former Arkansas Gov. Mike Huckabee, Ohio Gov. John Kasich and Kentucky Sen. Rand Paul all at 2%.

Photos:Donald Trump's rise

Photos:Donald Trump's rise

President-elect Donald Trump has been in the spotlight for years. From developing real estate and producing and starring in TV shows, he became a celebrity long before winning the White House.

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Photos:Donald Trump's rise

Trump at age 4. He was born in 1946 to Fred and Mary Trump in New York City. His father was a real estate developer.

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Trump, left, in a family photo. He was the second-youngest of five children.

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Photos:Donald Trump's rise

Trump, center, stands at attention during his senior year at the New York Military Academy in 1964.

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Photos:Donald Trump's rise

Trump, center, wears a baseball uniform at the New York Military Academy in 1964. After he graduated from the boarding school, he went to college. He started at Fordham University before transferring and later graduating from the Wharton School, the University of Pennsylvania's business school.

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Photos:Donald Trump's rise

Trump stands with Alfred Eisenpreis, New York's economic development administrator, in 1976 while they look at a sketch of a new 1,400-room renovation project of the Commodore Hotel. After graduating college in 1968, Trump worked with his father on developments in Queens and Brooklyn before purchasing or building multiple properties in New York and Atlantic City, New Jersey. Those properties included Trump Tower in New York and Trump Plaza and multiple casinos in Atlantic City.

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Trump attends an event to mark the start of construction of the New York Convention Center in 1979.

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Trump wears a hard hat at the Trump Tower construction site in New York in 1980.

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Trump was married to Ivana Zelnicek Trump from 1977 to 1990, when they divorced. They had three children together: Donald Jr., Ivanka and Eric.

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The Trump family, circa 1986.

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Trump uses his personal helicopter to get around New York in 1987.

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Photos:Donald Trump's rise

Trump stands in the atrium of the Trump Tower.

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Photos:Donald Trump's rise

Trump attends the opening of his new Atlantic City casino, the Taj Mahal, in 1989.

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Photos:Donald Trump's rise

Trump signs his second book, "Trump: Surviving at the Top," in 1990. Trump has published at least 16 other books, including "The Art of the Deal" and "The America We Deserve."

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Trump and singer Michael Jackson pose for a photo before traveling to visit Ryan White, a young child with AIDS, in 1990.

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Trump dips his second wife, Marla Maples, after the couple married in a private ceremony in New York in December 1993. The couple divorced in 1999 and had one daughter together, Tiffany.

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Trump putts a golf ball in his New York office in 1998.

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An advertisement for the television show "The Apprentice" hangs at Trump Tower in 2004. The show launched in January of that year. In January 2008, the show returned as "Celebrity Apprentice."

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Photos:Donald Trump's rise

A 12-inch talking Trump doll is on display at a toy store in New York in September 2004.

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Photos:Donald Trump's rise

Trump attends a news conference in 2005 that announced the establishment of Trump University. From 2005 until it closed in 2010, Trump University had about 10,000 people sign up for a program that promised success in real estate. Three separate lawsuits -- two class-action suits filed in California and one filed by New York's attorney general -- argued that the program was mired in fraud and deception. Trump's camp rejected the suits' claims as "baseless." And Trump has charged that the New York case against him is politically motivated.

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Trump attends the U.S. Open tennis tournament with his third wife, Melania Knauss-Trump, and their son, Barron, in 2006. Trump and Knauss married in 2005.

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Trump wrestles with "Stone Cold" Steve Austin at WrestleMania in 2007. Trump has close ties with the WWE and its CEO, Vince McMahon.

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For "The Apprentice," Trump was honored with a star on the Hollywood Walk of Fame in January 2007.

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Trump appears on the set of "The Celebrity Apprentice" with two of his children -- Donald Jr. and Ivanka -- in 2009.

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Trump poses with Miss Universe contestants in 2011. Trump had been executive producer of the Miss Universe, Miss USA and Miss Teen USA pageants since 1996.

Trump -- flanked by U.S. Sens. Marco Rubio, left, and Ted Cruz -- speaks during a CNN debate in Miami on March 10. Trump dominated the GOP primaries and emerged as the presumptive nominee in May.

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The Trump family poses for a photo in New York in April.

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Trump speaks during a campaign event in Evansville, Indiana, on April 28. After Trump won the Indiana primary, his last two competitors dropped out of the GOP race.

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Trump delivers a speech at the Republican National Convention in July, accepting the party's nomination for President. "I have had a truly great life in business," he said. "But now, my sole and exclusive mission is to go to work for our country -- to go to work for you. It's time to deliver a victory for the American people."

Trump apologizes in a video, posted to his Twitter account in October, for vulgar and sexually aggressive remarks he made a decade ago regarding women. "I said it, I was wrong and I apologize," Trump said, referring to lewd comments he made during a previously unaired taping of "Access Hollywood." Multiple Republican leaders rescinded their endorsements of Trump after the footage was released.

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Trump walks on stage with his family after he was declared the election winner on November 9. "Ours was not a campaign, but rather, an incredible and great movement," he told his supporters in New York.

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Trump is joined by his family as he is sworn in as President on January 20.

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Trump's lead in these national polls varies from 27 points in the most recent poll from Monmouth University to just five points in the NBC News/Wall Street Journal survey conducted early last week. Some of that difference stems from sampling -- the CNN/ORC Poll and the Monmouth poll measure opinions among registered voters who say they are Republicans or lean toward the Republican Party, and both found Trump with larger leads than some polls using a different sampling method.

There is also timing, with the Monmouth poll the only one conducted entirely after Trump released his proposal calling for a ban on allowing Muslims to enter the United States.

Still, each of the five polls included in the national CNN Poll of Polls shows Trump holding a lead larger than its margin of sampling error.

While the national polling shows significant volatility, the Iowa poll results show even greater variation from poll to poll.

According to the CNN Poll of Polls averaging the six most recent live-interviewer telephone polls, the race in Iowa is a tight one between Cruz (27%) and Trump (25%). Rubio and Carson follow here as well, with 13% and 12% respectively, while Bush (5%) and Paul (4%) lag behind, trailed by four candidates at 2% each: Christie, Fiorina, Huckabee and Kasich.

Photos:Moments from Ted Cruz's career

Photos:Moments from Ted Cruz's career

U.S. Sen. Ted Cruz, a Republican presidential candidate, speaks during a campaign rally at the Indiana State Fairgrounds on Monday, May 2.

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Cruz holds up the hand of Carly Fiorina at a campaign rally in Indianapolis on Wednesday, April 27. Cruz named Fiorina, a former presidential candidate, as his running mate.

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Cruz celebrates his Wisconsin primary win with his wife, Heidi, and Gov. Scott Walker in Milwaukee on Tuesday, April 5. Walker endorsed Cruz for the presidency.

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With his wife by his side, Cruz tours the Dane Manufacturing facility before speaking to workers in Dane, Wisconsin, on Thursday, March 24.

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Cruz speaks during the CNN Republican debate in Miami on Thursday, March 10.

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Cruz and his wife wave to the crowd at Liberty University after he announced his presidential candidacy in Lynchburg, Virginia, on March 23, 2015.

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Cruz speaks during the 2013 NRA Annual Meeting and Exhibits at the George R. Brown Convention Center on May 3, 2013, in Houston, Texas.

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Cruz poses with his wife, Heidi, and his daughters Caroline and Catherine.

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Cruz (left) fields questions from Bruce Rastetter at the Iowa Ag Summit on March 7, 2015, in Des Moines, Iowa. The event allows the invited speakers, many of whom are potential 2016 Republican presidential hopefuls, to outline their views on agricultural issue.

Sen. Patrick Leahy (right) escorts Loretta Lynch back from a lunch break as Cruz (left) sits nearby during her confirmation hearing before the Senate Judiciary Committee January 28, 2015, on Capitol Hill.

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Photos:Moments from Ted Cruz's career

Cruz greets supporters at the South Carolina Tea Party Coalition convention on January 18, 2015, in Myrtle Beach, South Carolina. A variety of conservative presidential hopefuls spoke at the gathering on the second day of a three-day event.

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Photos:Moments from Ted Cruz's career

Cruz (left) and then-Texas Governor Rick Perry stand together during a press conference at the front gate of Fort Hood about Iraq war veteran, Ivan Lopez, who killed three and wounded 16 before taking his own life on April 4, 2014, in Fort Hood, Texas.

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Photos:Moments from Ted Cruz's career

(Left to right) Sen. Lindsey Graham, Sen. John McCain and Cruz listen as President Barack Obama delivers the State of the Union address on January 28, 2014, in Washington, D.C.

Three of the six Iowa polls included here found Cruz with a significant lead over Trump, two found the two within margin of error of each other, and one found Trump ahead by a wide margin. The CNN/ORC poll which found Trump ahead is the oldest in the bunch, with interviews conducted between November 28 and December 6.

Surveying likely Iowa caucusgoers is one of the toughest challenges in election polling, as it is routinely one of the lowest turnout events in the entire presidential election process. In 2012 and 2008, only about 6% of the state's registered voters participated in the Republican caucuses, and whether turnout this time around will be similar is a question that can't be answered until the caucuses themselves are complete.

Some argue that Trump's appeal among those who are not regular participants in the caucus process will drive turnout higher, much as the hotly contested presidential race on the Democratic side in 2008 did for that party. Others say Trump's supporters' allegiances aren't strong enough to overcome the challenges inherent in participating in a caucus: Having to trudge out on a wintry night for several hours of political speeches and declare your support for your chosen candidate publicly.

In New Hampshire, a larger turnout means the task is somewhat easier, and the most recent polls are more closely aligned with each other. Five polls were included in the CNN Poll of Polls in New Hampshire, with the earliest including interviews conducted November 14 and the latest running through December 8.

Businessman Donald Trump announced June 16 at his Trump Tower in New York City that he is seeking the Republican presidential nomination. This ends more than two decades of flirting with the idea of running for the White House.

"So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement.

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Photos:Who's running for president?

Sen. Ted Cruz of Texas has made a name for himself in the Senate, solidifying his brand as a conservative firebrand willing to take on the GOP's establishment. He announced he was seeking the Republican presidential nomination in a speech on March 23.

"These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant."

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Photos:Who's running for president?

Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid.

"I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University.

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Photos:Who's running for president?

Hillary Clinton launched her presidential bid on April 12 through a video message on social media. The former first lady, senator and secretary of state is considered the front-runner among possible Democratic candidates.

"Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey."

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Photos:Who's running for president?

Sen. Bernie Sanders, an independent from Vermont who caucuses with Democrats, announced his run in an email to supporters on April 30. He has said the United States needs a "political revolution" of working-class Americans to take back control of the government from billionaires.

"This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26.

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The CNN Poll of Polls in New Hampshire finds Trump (26%) with a more than 2-to-1 advantage over his nearest competitor, Rubio, who at 12% is the only other candidate to average double-digits. Behind Rubio, a passel of candidates range in support from 7% to 9% -- Carson and Cruz each average 9%, Bush 8% and Kasich and Christie 7%.

That bunch-up around third place masks some clear trends that have developed in recent New Hampshire polling, Christie's numbers are on the rise, with the governor averaging 11% in the two polls conducted after Thanksgiving compared with 5% in the three conducted earlier in November.

Carson, meanwhile, has been losing steam, dropping from 11% in the pre-Thanksgiving polls to 6% in the polling conducted more recently. Bush, Rubio and Cruz have been roughly steady in the Granite State lately.